Images obtained by image pickup devices such as digital still cameras are deteriorated due to image blurs. The blurs of images are caused by a spherical aberration, a comatic aberration, field curvature, astigmatism, and the like. These aberrations may be represented by a PSF (Point Spread Function). An OTF (Optic Transfer Function) obtained by performing Fourier transform on the point spread function (hereinafter referred to as a “PSF”) is information on an aberration in a frequency space and is represented by a complex number. An absolute value of the optic transfer function (hereinafter referred to as an “OTF”), that is, an amplitude component is referred to as an MTF (Modulation Transfer Function), and a phase component is referred to as a PTF (Phase Transfer Function). An OTF of an image pickup optical system affects (deteriorates) an amplitude component and a phase component of an image. Therefore, in the image deteriorated by the influence of the OTF (hereinafter referred to as a “deteriorated image”), points of an object blur in an asymmetrical manner like a comatic aberration.
This case will be described with reference to FIGS. 23A to 23C. FIGS. 23A to 23C are diagrams schematically illustrating spread of the point spread function (PSF) in a plane which orthogonally intersects with a main light beam (which passes pupil of an optical system). In the plane shown in FIGS. 23A to 23C, lines which pass an optical axis and which orthogonally intersect with each other are determined as axes x1 and x2, and an angle θ defined by an arbitrary line which passes the optical axis and the axis x1 is determined as an azimuthal angle. Furthermore, when an origin of a coordinate axis of FIGS. 23A to 23C is determined as an image forming position of the main light beam, a direction represented by the azimuthal angle θ is determined as an azimuthal direction. The azimuthal direction includes a sagittal direction and a meridional direction and is an inclusive term of all directions including the angle θ direction.
As described above, the deterioration of the phase component (PTF) causes asymmetry in the PSF. Furthermore, the deterioration of the amplitude component (MTF) affects a degree of spread of the PSF for each azimuthal direction. FIG. 23A is a diagram schematically illustrating the PSF in which the comatic aberration is generated. When an optical system includes an optical axis which does not slant and a lens which has a rotation symmetry shape, a PSF in a field angle except for the optical axis is symmetric relative to a line which passes the optical axis and the main light beam, and therefore, the PSF has a line-symmetric shape. In FIG. 23A, the PSF is line symmetric relative to the axis x2.
FIG. 23B shows a PSF in a state in which a phase shift has not occurred. The PSF has a symmetry shape relative to the individual azimuthal directions. However, since amplitudes (MTFs) are different from each other, spreads of the PSF in the axes x1 and x2 directions are different from each other, that is, an asymmetry PSF is obtained. Note that the PSF on the optical axis does not have a phase shift when a manufacturing error is not taken into consideration and does not have azimuthal dependence of amplitude deterioration, and accordingly, a rotation-symmetry shape is obtained as shown in FIG. 23C. Specifically, as shown in FIGS. 23A and 23B, the PSF forms an asymmetric shape due to shifts of phases (PTFs) in the individual azimuthal directions and a difference between amplitudes (MTFs) of the azimuthal directions, and the asymmetric shape causes an image blur which prevents an image from being generated with high accuracy.
As a technique of correcting an image blur, in Patent Literature 1, a parameter α used to design an image restoration filter is determined as shown in Expression 1. By adjusting the adjusting parameter α, the image restoration filter which does not act (α=0) is changed to an inverse filter (α=1). Therefore, a degree of image restoration may be adjusted only using a single parameter within a range from an original captured image to an image which has been restored at maximum.
                              F          ⁡                      (                          u              ,              v                        )                          =                                                            α                ⁢                                                                  ⁢                                  H                  ⁡                                      (                                          u                      ,                      v                                        )                                                  *                                  +                  1                                            -              α                                                      α                ⁢                                                                                                H                      ⁡                                              (                                                  u                          ,                          v                                                )                                                                                                  2                                            +              1              -              α                                ×                      G            ⁡                          (                              u                ,                v                            )                                                          (                  Expression          ⁢                                          ⁢          1                )            Here, F(u, v) and G(u, v) represent a restoration image and a deteriorated image which have been subjected to Fourier transform, respectively.
Furthermore, as a filter which corrects an image blur so as to improve sharpness, a Wiener filter is known. A frequency characteristic M(u, v) of the Wiener filter is represented by Expression 2.
                              M          ⁡                      (                          u              ,              v                        )                          =                              1                          H              ⁡                              (                                  u                  ,                  v                                )                                              ⁢                                                                                      H                  ⁡                                      (                                          u                      ,                      v                                        )                                                                              2                                                                                                              H                    ⁡                                          (                                              u                        ,                        v                                            )                                                                                        2                            +                              SNR                2                                                                        (                  Expression          ⁢                                          ⁢          2                )            Here, H(u, v) denotes an optic transfer function (OTF). |H(u, v)| denotes an absolute value (MTF) of the OTF. SNR denotes an intensity ratio of a noise signal. Hereinafter, a process of restoring an image using the Wiener filter or the image restoration filter which is based on an optic transfer function (OTF) as disclosed in Patent Literature 1 is referred to as an image restoration process.